Problem: Simplify the following expression: $ t = \dfrac{-2z}{4z - 9} - \dfrac{-4}{7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2z}{4z - 9} \times \dfrac{7}{7} = \dfrac{-14z}{28z - 63} $ Multiply the second expression by $\dfrac{4z - 9}{4z - 9}$ $ \dfrac{-4}{7} \times \dfrac{4z - 9}{4z - 9} = \dfrac{-16z + 36}{28z - 63} $ Therefore $ t = \dfrac{-14z}{28z - 63} - \dfrac{-16z + 36}{28z - 63} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{-14z - (-16z + 36) }{28z - 63} $ Distribute the negative sign: $t = \dfrac{-14z + 16z - 36}{28z - 63}$ $t = \dfrac{2z - 36}{28z - 63}$